A197629 Number of ways to write n as the sum of two coprime, squarefree, composite, positive integers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 5, 0, 0, 0, 1, 0, 3, 1, 2, 0, 3, 0, 4, 1, 0, 1, 3, 0, 5, 0, 2, 0, 4, 0, 1, 2

Offset

1,41

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(29) is the first nonzero term since 29=15+14. The first nonzero even term is a(68) since 68=3(11)+5(7). Then the first even term with a value greater than one is a(86) since 86=3(7)+5(13) and 86=5(7)+3(17).

Prog

(MATLAB)
function [asubn]=ccsf(n)
% ccsf(n) returns the n-th term of the sequence of composite, coprime, square
% free sums of the integer n
r=0;
k=6;
while k<n/2,
if isprime(k)+isprime(n-k) == 0
if gcd(k, n-k) == 1
if prod(diff(factor(k)))*prod(diff(factor(n-k)))>0
r = r+1;
end
end
end
k=k+1;
end
asubn=r;
end
(PARI) a(n)=sum(k=4, (n-1)\2, gcd(k, n-k)==1&&!isprime(k)&&!isprime(n-k)&&issquarefree(k)&&issquarefree(n-k)) \\ Charles R Greathouse IV, Oct 18 2011

Crossrefs

Cf. A185279.

Sequence in context: A318983 A318982 A069851 * A198255 A290542 A359300

Adjacent sequences: A197626 A197627 A197628 * A197630 A197631 A197632

Keyword

nonn

Author

Jason Holland, Oct 16 2011

Status

approved